Small Strain Compatibility Conditions of an Elastic Solid in Cylindrical Coordinates

2013 ◽  
Author(s):  
D. Carlucci ◽  
N. Payne ◽  
I. Mehmedagic
Keyword(s):  
Elastic Solid ◽  
Small Strain ◽  
Cylindrical Coordinates ◽  
Compatibility Conditions ◽  
Strain Compatibility

scholarly journals The Reissner-Sagoci problem

1966 ◽  
Vol 7 (3) ◽  
pp. 136-144 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Plane Surface ◽  
Displacement Vector ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Cylindrical Coordinates ◽  
Circular Area ◽  
Image Position ◽  
Simple Equations

The statical Reissner-Sagoci problem [1, 2, 3] is that of determining the components of stress and displacement in the interior of the semi-infinite homogeneous isotropic elastic solid z ≧ 0 when a circular area (0 ≦ p ≦ a, z = 0) of the boundary surface is forced to rotate through an angle a about an axis which is normal to the undeformed plane surface of the medium. It is easily shown that, if we use cylindrical coordinates (p, φ, z), the displacement vector has only one non-vanishing component uφ (p, z), and the stress tensor has only two non-vanishing components, σρπ(p, z) and σπz(p, z). The stress-strain relations reduce to the two simple equationswhere μ is the shear modulus of the material. From these equations, it follows immediately that the equilibrium equationis satisfied provided that the function uπ(ρ, z) is a solution of the partial differential equationThe boundary conditions can be written in the formwhere, in the case in which we are most interested, f(p) = αρ. We also assume that, as r → ∞, uπ, σρπ and σπz all tend to zero.

Thermal Stress Analysis of a Multi-Layered Structure

2011 ◽  
Vol 467-469 ◽  
pp. 275-278
Author(s):  
Shiuh Chuan Her ◽  
Chin Hsien Lin
Keyword(s):  
Analytical Model ◽  
Layered Structure ◽  
Thermal Stresses ◽  
Closed Form Solution ◽  
Beam Theory ◽  
Form Solution ◽  
Bernoulli Beam ◽  
Compatibility Conditions ◽  
Strain Compatibility ◽  
Good Agreement

Analytical model based on the Bernoulli beam theory and strain compatibility conditions at the interfaces between the two layers have been developed to predict the distribution of thermal stresses within the multi-layered structure due to the mismatch of thermal expansion. The closed-form solution of thermal stresses related to the material properties and geometry were obtained. It is useful to provide a simple and efficient analytical model, so that the stress level in the layers can be accurately estimated. The analytical results are compared with finite element results. Good agreement demonstrates that the proposed approach is able to provide an efficient way for the calculation of the thermal stresses.

The internal stability of an elastic solid

2000 ◽  
Vol 80 (12) ◽  
pp. 2827-2840 ◽  
Author(s):  
J. W. Morris Jr, C. R. K Renn
Keyword(s):  
Elastic Solid ◽  
Internal Stability

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Sensitive Mechanocontrolled Luminescence in Cross-Linked Polymer Films

2019 ◽  
Author(s):  
Ayumu Karimata ◽  
Pradnya Patil ◽  
Eugene Khaskin ◽  
Sébastien Lapointe ◽  
robert fayzullin ◽  
...  
Keyword(s):  
Mechanical Stress ◽  
Polymer Films ◽  
Soft Matter ◽  
Small Strain ◽  
Visual Methods ◽  
Photoluminescence Intensity ◽  
Stimuli Responsive ◽  
Responsive Materials ◽  
Highly Sensitive ◽  
Mechanical Stretching

Direct translation of mechanical force into changes in chemical behavior on a molecular level has important implication not only for the fundamental understanding of mechanochemical processes, but also for the development of new stimuli-responsive materials. In particular, detection of mechanical stress in polymers via non-destructive methods is important in order to prevent material failure and to study the mechanical properties of soft matter. Herein, we report that highly sensitive changes in photoluminescence intensity can be observed in response to the mechanical stretching of cross-linked polymer films when using stable, (pyridinophane)Cu-based dynamic mechanophores. Upon stretching, the luminescence intensity increases in a fast and reversible manner even at small strain (< 50%) and applied stress (< 0.1 MPa) values. Such sensitivity is unprecedented when compared to previously reported systems based on organic mechanophores. The system also allows for the detection of weak mechanical stress by spectroscopic measurements or by direct visual methods.<br>

The study of the process of evolution of the jet under outflow of water from the supercritical state through a thin nozzle

2016 ◽  
Vol 11 (1) ◽  
pp. 66-71 ◽  
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Stationary Process ◽  
Supercritical State ◽  
System Of Differential Equations ◽  
Jet Formation ◽  
Cylindrical Coordinates ◽  
Initial Stage ◽  
Supersonic Regime ◽  
Water Outflow ◽  
Thin Nozzle ◽  
Supercritical Temperature

The dynamics of the water outflow from the initial supercritical state through a thin nozzle is studied. To describe the initial stage of non-stationary process outflow the system of differential equations of conservation of mass, momentum and energy in a two-dimensional cylindrical coordinates with axial symmetry is used. The spatial distribution of pressure and velocity of jet formation was received. It was established that a supersonic regime of outflow at supercritical temperature of 650 K is formed, which have a qualitative agreement for the velocity compared with the Bernoulli analytical solution and the experimental data.

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